A new method of nonlinear computer image processing is presented and tested on theoretically simulated images. The test images were calculated with the multislice method. With this new method of image processing the phase and amplitude of the specimen transmission function may be reconstructed from a defocus series of conventional bright field transmission electron micrographs. In this paper (the first of a two-part report) this new method is found to work with simulated images and in a companion paper (the second part of this report) it is also found to work with actual experimental micrographs. In each case, a moderately significant increase in resolution has been obtained.